Dimensions added using MeasureIt addon not appearing in final render
If you click on the View menu of the viewport area of interest, you can choose Viewport Render Image option.
Disabling overlays  keps the measureIt overlays, so you can use that to your advantage:


In order to get your measurements rendered, all you would have to do is:

Click on the Render button in the Render panel which is going to render your measurements as a separate image based on the active camera
Open up a new Compositor window or just switch the workspace to Compositing, add an Image as well as an Alpha Over node
Set the image for Image node to generated image by the MeasureIt add-on
Plug your rendering into the upper socket and the generated image into the foreground (lower) socket of the Alpha Over node


Also have a look into the manual: https://docs.blender.org/manual/en/latest/addons/3d_view/measureit.html.